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MaplePrimes Activity

These are questions asked by itsme


> restart:
> int(exp(I*x)/x,x=-infinity..infinity,CauchyPrincipalValue)
                                                                                                   Pi I

> int(exp(I*3*x)/x,x=-infinity..infinity,CauchyPrincipalValue)
                                                                                                   Pi I

> int(exp(I*k*x)/x,x=-infinity..infinity,CauchyPrincipalValue) assuming k::positive;
                                                                                                  2 I Pi

I would expect the last line to also give me Pi I

Mathematica gives a Pi I via:

FullSimplify[Integrate[Exp[I k x]/x, {x, -\[Infinity], \[Infinity]}, PrincipalValue->True, Assumptions->{k>0}],  Assumptions->{k>0}]

Any idea what this could be?



Say I have an expression like this:


I can factor out x,t and get an expected result:
collect(a0, [x,t]);

But how would I do it if I want to force Maple to act on the argument of exp?


This doesn't work:
collect(a1, [x,t])

This will do what I want for this expression but maybe not in general:


I would like to ask maple to "recognize" a Fourier transform in a (possibly complicated) expression.

Maple defines a Fourier transform in this way:
convert(fourier(f(x), x, k), Int);

So if f(x)=1 we should get something that is proportional to Dirac(k), which we do:
fourier(1, x, k);

...but given an expression
exp1:=Int(exp(-I*x*k), x = -infinity .. infinity);

... how would tell...

I am trying to see if Maple can help me find a closed form for an infinite series. I do this:



s:=Sum(n^2/((Pi^2*n^2+beta^2*epsilon^2)*(exp(n))^4), n = 1 .. infinity);



Maple returns with:

I often have large matrices and have to grab only every nth column or row (for plotting

for example). So far I've been doing it this way:

nthColumns:=proc(v_m, v_n)  
v_m[..,[seq(i, i=1..rtable_size(v_m)[2], v_n)]]
nthRows:=proc(v_m, v_n) 
 v_m[[seq(i, i=1..rtable_size(v_m)[1], v_n)],..]

A := LinearAlgebra:-RandomMatrix(20, 20, outputoptions = [datatype = float[8]]);
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